The commutative property in mathematics is the property states that the change in the order of numbers in an addition or multiplication operation does not change the sum or the product respectively. It means we can change the position or swap the numbers when adding or multiplying any two numbers but that will not affect the result. Commutative property can be applied only for addition and multiplication processes. This is one of the most important properties used in mathematics. The origin of the word commutative is from the word ‘commute’ that means to switch or move around. Therefore, the literal meaning of the word indicates that by swapping the positions of the integers, we expect to get the same result.
Commutative Property of Addition
As per the commutative property of addition, a set of numbers can be added in any order, and the result will be the same. In other words, the numerical value of the sum will not change even if the positions of the numbers are changed. For example, if we add two numbers, in whatever order they are placed, the answer will be the same. Let A and B are two integers, then as per commutative property of addition, A + B = B + A
Commutative Property of Multiplication
The commutative property for multiplication states that when two or more integers are multiplied, the product will remain unchanged irrespective of the order of the numbers being multiplied. This means while multiplying two numbers, even if we interchange the position of numbers, we get the same results. For example, if A and B are two integers, then as per the commutative property of multiplication, (A × B) = (B × A).
Facts of Commutative Property
- It is only applicable for two arithmetic operations: Addition and Multiplication
- By changing the order of numbers, the result remains unchanged
- For integers A and B, the Commutative property of addition means, A + B = B + A
- For integers A and B, the Commutative property of multiplication means, A x B = B X A
What is Distributive Property?
The distributive property in mathematics signifies a property in which the operation involves dividing or distributing something. This property is also known as the distributive property of addition (or subtraction) over multiplication.
We can apply the distributive property when a number is multiplied by the sum (or difference) of two numbers. In this case, the first number can be said to be distributed to both of those numbers and multiplied by each of them separately. Then adding (or subtracting) the two products will give the result which is the same as the multiplication of the first number by the sum (or difference) of those two numbers.
The distributive property can be best explained by an expression involving three numbers A, B, and C. The expression is given in the form A (B + C) or A (B-C). Then it will be resolved as A (B + C) = A* B + A * C or A (B – C) = A *B – A* C. This means A is distributed among the other two numbers B and C and hence it is called the distributive property of addition (or subtraction) over multiplication.
For example, for the expression 5 (3 + 7), we have to multiply 5 by the sum of 3 and 7.
We can solve the expression using the distributive property. We will first multiply 3 and 7 respectively by 5 and then add the products. Thus, the multiplication of 5 x 3 and 5 X 7 will be performed and two products are added to get the solution. Therefore, 5(3+7) = (5 X 3) + (5 x 7) = 15 + 35 = 50. This is the same result as 5 multiplied by the sum of 3 and 7. You can visit here to know about the rtsnet. On the other hand, you can also get more essential info on mynewsport. Here is the best news portal newstheater where you can get the latest news around the world coschedules
